Math Emeritus Sci Advisor Thanks PF Gold P: 39,491 There is no "extra z-axis". There is no z-axis at all! The level curves you are asked to draw are in the xy-plane. Graph $(x^2-2y+6)/(3x^2+y)= 0$ and $(x^2-2y+6)/(3x^2+y)= 1$. The first is easy- it is the same as the graph of $x^2- 2y+ 6= 0$ which is just the parabola $y= (1/2)x^2+ 3$. The second is not much harder: $x^2- 2y+ 6= 4x^2+ y$ or $y= 6- 3x^2$, also a parabola.